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cyclic n.  and  hexagonal n.

First numbers that belong to both sets:

1, 15, 91, 435, 561, 703, 1891, 2701, 3655, 5151, 8911, 9453, 10011, 10585, 12403, 15051, 15753, 16471, 18721, 22791, 23653, 26335, 35245, 38503, 39621, 49141, 50403, 59685, 62481, 69751, 77421, 79003, 88831, 93961, 99235, 104653, 110215, 115921, 121771, 125751, 129795, 133903, 144453, 146611, 153181, 157641, 159895, 188191, 205761, 218791, 226801, 229503, 243253, 248865, 257403, 269011, 277885, 286903, 314821, 334153, 337431, 344035, 364231, 374545, 385003, 392055, 406351, 417241, 435711, 439453, 458403, 473851, 485605, 497503, 521731, 534061, 542361, 571915, 597871, 624403, 637885, 651511, 665281, 688551, 693253, 697971, 721801, 736291, 765703, 795691, 826255, 836571, 841753, 873181, 889111, 905185, 915981, 921403, 926841, 954271, 970921, 982101, 993345, 1004653, 1027461, 1033203, 1038961, 1056331, 1073845, 1109305, 1127251, 1145341, 1181953, 1276003, 1295245, 1301691, 1314631, 1334161, 1353835, 1373653, 1393615, 1474903, 1495585, 1516411, 1537381, 1551441, 1558495, 1601155, 1622701, 1688203, 1755001, 1800253, 1807851, 1830741, 1869211, 1884711, 1892485, 1963171, 1987021, 2035153, 2133145, 2158003, 2166321, 2208151, 2233441, 2284453, 2318781, 2362051, 2388205, 2467531, 2521135, 2548153, 2575315, 2602621, 2630071, 2639253, 2685403, 2722611, 2741311, 2769481, 2826253, 2854855, 2912491, 2970703, 3029491, 3059101, 3118753, 3168903, 3178981, 3209311, 3239785, 3270403, 3301165, 3332071, 3363121, 3425653, 3488761, 3531153, 3584503, 3616705, 3627471, 3649051, 3681541, 3736011, 3812941, 3846151, 3879505, 3913003, 3924201, 3980431, 4014361, 4048435, 4082653, 4186171, 4220965, 4255903, 4326211, 4373403, 4397095, 4432753, 4504501, 4686391, 4760155, 4797253, 4871881, 4909411, 4984903, 5022865, 5060971, 5099221, 5150445, 5176153, 5214835, 5292631, 5357901, 5371003, 5449951, 5489641, 5556111, 5569453, 5690251, 5730805, 5744355, 5771503, 5825991, 5894461, 5977153, 6018715, 6102271, 6186403, 6228685, 6313681, 6327903, 6442255, 6456621, 6485401, 6528691, 6557631, 6615703, 6703291, 6747301, 6850551, 6880195, 6969511, 7014385, 7104565, 7134753, 7149871, 7195321, 7378561, 7424731, 7471045, 7517503, 7533021, 7564105, 7610851, 7673403, 7751953, 7783485, 7830903, 7846741, 7894351, 7942105, 7990003, 8006001, 8086231, 8134561, 8231653, 8378371, 8476903, 8526385, 8576011, 8625781, 8725753, 8826301, 8978203, 9080191, 9131401, 9165621, 9182755, 9234253, 9337681, 9493903, 9546265, 9810235, 9863461, 9916831, 9934653.